Hyperspectral Unmixing using a Structured Linear Mixing Model with Additive Spectral Variability

Linear hyperspectral unmixing aims at retrieving pure material spectra present in an observed scene and their associated abundance fractions in each pixel. In most practical situations, hyperspectral images are affected by spectral variability (SV) also known as intra-class variability, which is caused by different physical phenomena including atmospheric effects, intrinsic variability of the pure materials and illumination or topographic changes. Nevertheless, the standard hyperspectral unmixing methods that rely on the Linear Mixing Model (LMM) do not consider these phenomena. Thus, neglecting them will spread errors throughout the linear hyperspectral unmixing process. To avoid this problem, this paper proposes two hyperspectral unmixing algorithms dedicated to a parametric model called Structured Additive Variability LMM (SAV-LMM). This mixing model handles SV in an additive manner by incorporating two terms into the standard LMM. Moreover, the designed algorithms are based on Nonnegative Matrix Factorization (NMF) and optimize a cost function which integrates additional penalization accounting for SV. Furthermore, a novel improved initialization scheme, which takes SV into account, is proposed. Experiments conducted on both synthetic and real datasets show the effectiveness of the proposed algorithms for linearly unmixing hyperspectral images with SV compared to the tested state-of-the-art methods.